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Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 989 (4 self)
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the rootmeansquare deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums of products of corresponding coordinates of the points. 1.
A Tutorial on Visual Servo Control
 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION
, 1996
"... This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review ..."
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Cited by 839 (26 self)
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This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, positionbased and imagebased systems, are then discussed. Since any visual servo system must be capable of tracking image features in a sequence of images, we include an overview of featurebased and correlationbased methods for tracking. We conclude the tutorial with a number of observations on the current directions of the research field of visual servo control.
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 660 (8 self)
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A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subsetsubset matching. A leastsquares technique is used to estimate 3D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
A Survey of Medical Image Registration
, 1998
"... The purpose of this chapter is to present a survey of recent publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods The statistics of t ..."
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Cited by 548 (5 self)
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The purpose of this chapter is to present a survey of recent publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods The statistics of the classification show definite trends in the evolving registration techniques, which will be discussed. At this moment, the bulk of interesting intrinsic methods is either based on segmented points or surfaces, or on techniques endeavoring to use the full information content of the images involved.
Pose estimation from corresponding point data
 IEEE Transactions on Systems, Man and Cybernetics
, 1989
"... AbstracrSolutions for four different pose estimation problems are presented. Closed form leastsquares solutions are given to the over constrained ZDZD and 3D3D pose estimation problems. A globally convergent iterative technique is given for the 2D perspective projection3D pose estimation ..."
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Cited by 199 (2 self)
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AbstracrSolutions for four different pose estimation problems are presented. Closed form leastsquares solutions are given to the over constrained ZDZD and 3D3D pose estimation problems. A globally convergent iterative technique is given for the 2D perspective projection3D pose estimation problem. A simplified linear solution and a robust solution to the 2D perspective projectionZD perspective projection pose estimation problem are also given. Simulation experiments consisting of millions of hia ls having varying numbers of pairs of corresponding points, varying signal to noise ratio (SNR) with either Gaussian or uniform noise provide data suggesting that accurate inference of rotation and translation with noisy data may require corresponding point data sets having hundreds of corresponding point pairs when the SNR is less than 40 dB. The experiment results also show that robust technique can suppress the effect of blunder data that come from outliers or mismatched points. I.
Comparison and evaluation of retrospective intermodality brain image registration techniques
 JOURNAL OF COMPUTER ASSISTED TOMOGRAPHY
, 1997
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Fast and Globally Convergent Pose Estimation From Video Images
, 1998
"... Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effecti ..."
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Cited by 151 (6 self)
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Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers. ChienPing Lu, Silicon Graphics Inc. cplu@engr.sgi.com y Greg Hager, Department of Computer...
Object Detection Using the Statistics of Parts
, 2004
"... In this paper we describe a trainable object detector and its instantiations for detecting faces and cars at any size, location, and pose. To cope with variation in object orientation, the detector uses multiple classifiers, each spanning a different range of orientation. Each of these classifiers ..."
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Cited by 142 (2 self)
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In this paper we describe a trainable object detector and its instantiations for detecting faces and cars at any size, location, and pose. To cope with variation in object orientation, the detector uses multiple classifiers, each spanning a different range of orientation. Each of these classifiers determines whether the object is present at a specified size within a fixedsize image window. To find the object at any location and size, these classifiers scan the image exhaustively. Each classifier is based on the statistics of localized parts. Each part is a transform from a subset of wavelet coefficients to a discrete set of values. Such parts are designed to capture various combinations of locality in space, frequency, and orientation. In building each classifier, we gathered the classconditional statistics of these part values from representative samples of object and nonobject images. We trained each classifier to minimize classification error on the training set by using Adaboost with ConfidenceWeighted Predictions (Shapire and Singer, 1999). In detection, each classifier computes the part values within the image window and looks up their associated classconditional probabilities. The classifier then makes a decision by applying a likelihood ratio test. For efficiency, the classifier evaluates this likelihood ratio in stages. At each stage, the classifier compares the partial likelihood ratio to a threshold and makes a decision about whether to cease evaluation—labeling the input as nonobject—or to continue further evaluation. The detector orders these stages of evaluation from a lowresolution to a highresolution search of the image. Our trainable object detector achieves reliable and efficient detection of human faces and passenger cars with outofplane rotation.
Nonrigid point set registration: Coherent Point Drift (CPD)
 IN ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 19
, 2006
"... We introduce Coherent Point Drift (CPD), a novel probabilistic method for nonrigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with ..."
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Cited by 141 (0 self)
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We introduce Coherent Point Drift (CPD), a novel probabilistic method for nonrigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the nonrigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex nonlinear nonrigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points.